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Vocabulary
Add / Subtract Rational Expression
Multiply / Divide Rational Expression
Solve Rational Equations
Word Problems
100
an algebraic fraction with a numerator and a denominator that are polynomials
rational expression
100
　1/y + 1/x
x/xy+y/xy (x+y)/xy NPV: X≠0, Y≠0
100
(3-p)/(p-3)
(3-p)/-(3-p) =-1 npv: p≠3
100
How to solve the rational equation 2/x=x/3
x=2
100
The sum of two numbers is 18. The sum of their reciprocals is 1/4. What are the two numbers?
x=one number. 1/x+1/(18-x)=1/4 x1=6, x2=12
200
any value for a variable that makes an expression undefined
Non-permissible value
200
7/3x + 3/x^2
7x/3x^2+9/3x^2 (7x+9)/3x^2 X≠0
200
[(7k-1)/3k]*[1/(1-7k)]
[(7k-1)/3k]*[1/-(7k-1)] =1/-3k Npv:1/7,0
200
How to solve the rational equation (x-1)/15=2/5
(x-1)/15=2*3/5*3 (x-1)/15=6/15 x-1=6 x=7
200
Frank likes to drive very quickly. His workplace is 80km away from his home. When he was going to work one day, his average speed exceeded the speed limit by 15km/h. He spotted police ahead of him on the way, so he took a detour of 20km and successfully avoided the police. On his way home he drove at the speed limit on his regular route. On that day, Frank spent exactly the same amount of time going to work and going home. What is the speed limit?
(80+20)/(x+15)=80/x x=60
300
an equation containing at least one rational expression
Rational equation
300
(9/3xy^2) - [(2x + 3)/2x^2y]
3/xy^2-2x+3/2x^2y (3x-4x^3y^2-3y)/2x^2y^2 NPV: X≠0, Y≠0
300
[(a+3)/(a+1)]*[(a^2-1)/(a^-9)]
[(a+3)/(a+1)]*[(a+1)(a-1)/(a+3)(a-3)] =(a-1)/(a-3) Npv:3,-3,1,-1
300
How to solve the rational equation 10/［x(x-2)]+4/x=5/(x-2)
10/[x(x-2)]+[4(x-2)]/[x(x-2)]=5x/[x(x-2)] 10/[x(x-2)]+(4x-8)/[x(x-2)]=5x/[x(x-2)] 10+4x-8=5x x=2 x=2 is NPV, so no solution
300
A few ogres decided they would each pay the same amount of coins for a trip to Gadgetzan. Before the trip, two ogres died in a battle. The remaining ogres each had to pay 1 extra coin for them to make the trip. If the total cost of the trip was 24 coins, how many ogres wanted to go on the trip before the battle?
x=number of ogres. 24/(x-2)-24/x=1 x1=8, x2=-6 (reject) 8 ogres.
400
The top number in a fraction. Shows how many parts we have. (The bottom number is the Denominator and shows how many equal parts the item is divided into.)
numerator
400
1/x/y^2-9 + 4/y/y+3
1/x(y^2-9)+4/y(y+3) y+4x(y-3)/xy(y^2-9) (y+4xy-12x)/xy(x+3)(x-3) NPV: X≠3,-3,0 Y≠3,-3,0
400
(x^2+2xy+y^2)/(x^2-2xy+y^2) ÷ 2x^2+3xy+y^2/x(x-y)
[(x+y)^2/(x-y)^2] * [x(x-y)/(2x+y)(x+y)] (x^2+xy)/(2x^2-y^2) Npv: x≠y, y≠-2x, x≠-y, x≠0, y≠2^(1/2)x, y≠-2^(1/2)x
400
How to solve the rational equation x/(x-2)+1/(x-4)=2/(x^2-6x+8)
(x^2-4x)/[(x-2)(x-4)]+(x-2)/[(x-2)(x-4)]=2/[(x-2)(x-4)] (x^2-4x)+(x-2)=2 x^2-3x-4=0 (x-4)(x+1)=0 x1=4 x2=-1
400
Boogeymonsters like eating almost anything. Two Boogeymonsters have been eating a kodo for five minutes when one of them is transformed into a squirrel by Tinkmaster Overspark and no longer likes eating kodos. So the squirrel jumped onto the remaining Boogeymonster while he was still eating. It took the creatures 15 minutes in total to finish eating the poor kodo. How long does it take one Boogeymonster to eat one kodo?
x=time needed for one Boogeymonster to eat one raptor 5*(1/x)*2+(1/x)*10=1 x=20
500
he least common multiple of the denominators of a set of fractions. It simplifies adding, subtracting, and comparing fractions
LCD(Lowest common denominators)
500
[9/(x+4)]+[(x-2)/(x^2-16)]
9(x-4)/(x+4)(x-4)+(x-2)/x^2-16 (10x-38)/x^2-16 NPV: X≠4,-4
500
[4x-5+(4x^2-x)/(x-1)]/[2x+1+(x+1)/(x-1)]
{[(4x-5)(x-1)+4x^2-x]/(x-1)}/{[(2x+1)(x-1)+x+1]/(x-1)} {[(4x-5)(x-1)+4x^2-x]/(x-1)}*{(x-1)/[(2x+1)(x-1)+x+1]} (8x^2-10x+5)/2x^2 npv: 0, [1+5^(1/2)]/2, [1-5^(1/2)]/2, 1, -2
500
How to solve the rational equation 3/(X+2)-1/X=1/5X
15X/[5X(X+2)]-(5X+10)/[5X(X+2)]=(X+2)/[5X(X+2)] 15X-(5X+10)=X+2 10X-10=X+2 9X=12 X=12/9=4/3
500
Two hoses together fill a pool in 216 minutes. If only hose A is used, the pool fills in 6h. The hoses drain as fast as filling. How long would it take to fill the pool if hose A is used to fill, and hose B is used to drain at the same time?
x=time needed for hose B to fill the pool 18/5(1/6+1/x)=1 x=9 1/(1/6-1/9)=18h